Antonio J. Calderón Martín ; Boubacar Dieme
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Certain partitions on a set and their applications to different classes of graded algebras
cm:9540 -
Communications in Mathematics,
July 15, 2021,
Volume 29 (2021), Issue 2 (Special Issue: 3rd International Workshop on Nonassociative Algebras in Málaga)
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https://doi.org/10.2478/cm-2021-0021
Certain partitions on a set and their applications to different classes of graded algebrasArticle
Authors: Antonio J. Calderón Martín 1,2; Boubacar Dieme 3,4
Let (A, u) and (B, b) be two pointed sets. Given a family ofthree maps F = {f1 : A → A; f2 : A × A → A; f3 : A × A → B}, thisfamily provides an adequate decomposition of A \ {u} as the orthogonaldisjoint union of well-described F-invariant subsets. This decompositionis applied to the structure theory of graded involutive algebras, gradedquadratic algebras and graded weak H∗-algebras.